cp's OEIS Frontend

A088242 Values of x, where x^2 + xy + y^2 = p (x is a prime of the form 6n + 1 (A002476).

%I A088242 #15 Jun 16 2025 15:10:18
%S A088242 1,1,2,1,3,1,4,2,1,3,3,2,5,6,3,5,1,3,4,7,2,1,6,5,1,9,7,6,1,3,10,8,3,9,
%T A088242 4,7,11,8,1,11,5,7,1,2,7,9,4,13,5,8,1,3,9,5,14,11,9,8,11,3,13,12,7,10,
%U A088242 1,15,2,6,14,13,4,10,3,13,7,17,3,7,9,13,8,11,16,15,6,3,12,17,7,9,1,3,16
%N A088242 Values of x, where x^2 + xy + y^2 = p (x<y) is a prime of the form 6n + 1 (A002476).
%H A088242 Robert Israel, <a href="/A088242/b088242.txt">Table of n, a(n) for n = 1..10000</a>
%p A088242 R:= NULL: count:= 0:
%p A088242 for k from 1 while count < 100 do
%p A088242   p:= 6*k+1;
%p A088242   if not isprime(p) then next fi;
%p A088242   S:= select(t -> subs(t,x) > 0 and subs(t,x) < subs(t,y), [isolve(x^2+x*y+y^2=p)]);
%p A088242   S:= map(t -> subs(t,x), S);
%p A088242    R:= R,op(S); count:= count+1;
%p A088242 od:
%p A088242 R; # _Robert Israel_, Jun 16 2025
%t A088242 Reap[For[n = 1, n <= 200, n++, If[PrimeQ[p = 6 n + 1], s = Solve[x^2 + x y + y^2 == p && 0 < x < y, {x, y}, Integers]; Sow[x /. s[[1]]]]]][[2, 1]] (* _Jean-François Alcover_, Mar 07 2020 *)
%Y A088242 Cf. A002476, A088241, A088243, A088296, A088298, A088299, A088977.
%K A088242 nonn
%O A088242 1,3
%A A088242 _Lekraj Beedassy_, Nov 03 2003
%E A088242 More terms from _Ray Chandler_, Nov 04 2003